(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let V=Mn(F) be the space of all nxn matrices over F; define TA=(1/2)(A+transpose(A)) for A in V.

Verify that T is not only a linear operator on V, but is also a projection.

2. Relevant equations

A is a projection when A squared=A.

3. The attempt at a solution

I don't see how this works since clearly (1/2)(A+transpose(A)) squared does not equal (1/2)(A+transpose(A)) for all matrices.

What am I doing wrong?

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# Homework Help: Show this is a projection on a vector space

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